Prime Factorisation

Prime Factorisation is finding the prime numbers which form the product i.e. a particular number. It is basically finding the prime numbers (or the numbers that do not have any factors) of the given number, which is the product of the two or more prime numbers.
Solved Example

1.

In the above example, we saw that 90 is a product of multiplication between the prime numbers – 2, 3 and 5. Hence, finding 2, 3, and 5 as the numbers responsible for the product number 90 is known as prime factorization. This way of illustrating prime factorization is known as ‘factor tree’.
______________________________________________________________________
2. Let’s take some more examples to clarify the concept.
Let’s take the number 36.
We will begin the factorization with the lowest prime number 2.
36/2 = 18.
Since, 18 is an even number we will further divide 18 by 2, i.e.
18/2 = 9. Now, 9 is not divisible by 2, so we move on to the next prime number 3, and divide the number with 3, i.e. 9/3 = 3.
Thus, the prime factorization of number 36 = 2 x 2 x 3 x 3.
______________________________________________________________________
3. Let’s take the number 980.
We will begin the factorization with the lowest prime number i.e. 2.
So, 980/2 = 490. We will again divide 490 by 2 as 490 is an even number, and that gives us the result
490/2 = 245. Applying the divisibility rule of the next prime number i.e. 3, we get that 245 is not divisible by 3 and we move on to the next prime number 5.
245/5 = 49 gives us the answer 49. Moving on to the next prime number 7, we will see that 49/7 = 7, and we stop here.
Hence we come to know that – 980 = 2 x 2 x 5 x 7 x 7